Recently, a math professor, with a very impressive set of mathematical papers. made a comment that took me by surprise. I am very open to the feedback. I wanted to open it up here to see what others think.

The professor pointed out that I was duplicating standard reasoning in my question. He suggested that I not think about the Collatz Conjecture at all. He suggested that if I do decide to reject this advice, at least read lots of previous work on the problem so as not to merely redo it (for the record, I've been going through each of the articles referenced in the Wikipedia article, I am reading through Terence Tao's paper on Collatz Conjecture as I have time).

I told the professor that I would be glad to delete the question if he could point me to a paper that covered the same topic (If anyone here points out a paper on the topic of divergent collatz sequences that covers the same ground as my question, I am very glad to delete the question).

I think that implicit in the comment is a compliment. There's an assumption that my mathematical understanding is strong enough that there was no need for my question. The assumption is that if I read more papers on the topic, I might be able to ask a question that did not involve standard reasoning (to be honest, it is my greatest regret that I did not pursue a masters in mathematics -- and that I have so many gaps in my understanding). I agree that spending time on the Collatz Conjecture will most likely not lead to any significant mathematical output. Unfortunately, I suspect that any other topic that I chose to spend my time on would suffer the same fate. I love learning and growing my mathematical ability. I have a very long way to go before my mathematical output merits getting published.

I wondered what others thought about this comment. This is great advice for the professional mathematician and the promising mathematic student. For me, my goal is to learn as much as possible and continuously improve the quality of my questions. While this is my goal, it is true (and I think that this is the professor's point), I may not be accomplishing this goal as much as I should.

I am not clear how to find math papers that fit my questions. I can go to Google. I can read through a Wikipedia article. I can go to Google Scholar. I buy books such as this. I would be glad if anyone has thoughts. How do mathematicians find out if a relevant paper has already been published?

I am a math amateur. I am active on this web site solely because I am trying to learn to think more clearly about mathematics. Being active on this site humbles me and helps me to appreciate the beauty of mathematics.

When I pose a question on this site, I typically spend 2-3 hours writing it, checking the results, and making sure that there are no typos or mistakes in reasoning. Typically, my questions reveal mistakes in my reasoning or assumptions that are not valid. For this reason, I get great satisfaction and value from reading comments and the answers given to my questions.

I greatly enjoy learning and really appreciate the MSE community for supporting me in my pursuit to better understand number theory.

As far as topics, I do not really choose what I am interested in. I wish I could. Certain topics are interesting to me. Others are not. I am a software engineer by profession. Programming comes very easy to me. Mathematics which is more interesting to me does not. I get so many mathematical ideas in my head that if I could somehow do a better job of filtering out the "standard reasoning", then perhaps, I might greatly improve the questions that I ask. They seem great until I type them up as questions.

50% of the questions that I start to ask, I delete before I finish writing them up because I change my mind on whether it was worth asking.

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    $\begingroup$ Your question seems to be regarding a comment that you were "duplicating standard reasoning" : you'll have to find out if this is true, if I have to be honest, but if it's a professor addressing you then you will know that they are probably spot on. Now, there are many, many papers on the Collatz conjecture other than Tao's. For example, there are probabilistic approaches, linear programming approaches, function theory approaches, what not... and being someone who is more than willing to ratify their stance, I'll be attaching some papers below that I think you should read on the CC, but my ... $\endgroup$ Commented Jun 13, 2021 at 3:30
  • $\begingroup$ ... take on this situation is that duplicating standard reasoning can be done if you think the reasoning isn't commonly seen around, or hasn't been done on one of your posts before. If you are asking many questions on one subject, you can afford to do your working in one of them and then attach the same question to every other post. See, the problem is the word "standard" : what is standard to someone isn't to the other person! So the professor is saying this because they've observed your previous questions or your argument is a very common one even outside Collatz-based math. To the papers... $\endgroup$ Commented Jun 13, 2021 at 3:34
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    $\begingroup$ See here for probabilistic ideas, here and here for iterative-theory and clustering based arguments, here for a linear algebraic approach, here for a complex-analytic approach. Then you can use the associated links to browse. Personally, asking questions on CC in MSE will require excellent background knowledge. I am willing to assist. $\endgroup$ Commented Jun 13, 2021 at 3:45
  • $\begingroup$ Awesome, Teresa! Thanks very much! $\endgroup$ Commented Jun 13, 2021 at 4:14
  • $\begingroup$ You are welcome! Once you read these papers you will certainly feel better about your own background for sure, and can hold your own against some professionals. $\endgroup$ Commented Jun 13, 2021 at 4:32
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    $\begingroup$ I think for a math amateur the way to go is to type Collatz into the search box on math.stackexchange and wade through the questions that have been asked about it already. You'll probably find good information, at your level, about the math, and pointers to the literature that you might not have been aware of. [The question to which OP refers is math.stackexchange.com/questions/4171307/… $\endgroup$ Commented Jun 13, 2021 at 5:36
  • $\begingroup$ Thanks, @GerryMyerson I've been finding great leads on MSE! I'll make a point to iterate the articles found in the search box and tagged with collatz. $\endgroup$ Commented Jun 13, 2021 at 5:55
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    $\begingroup$ The question that you mentioned has 0 downvotes on it and 0 close votes. I don't think anyone wanted you to delete it, I think the user was just giving some friendly advice :) $\endgroup$
    – Asinomás
    Commented Jun 14, 2021 at 14:10
  • $\begingroup$ Great point, @Yorch. I think you are right that it was meant as friendly advice. I think because it was a math professor giving the advice, I felt more concerned and wanted to do the right thing. $\endgroup$ Commented Jun 14, 2021 at 16:12


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